Three solutions for a nonlocal Dirichlet boundary value problem involving the p(x)-Laplacian

Abstract

In this article, we consider a nonlocal problem involving the p(x)-Laplacian of the type Applying a three critical points theorem from Bonanno [A critical points theorem and nonlinear differential problems, J. Global Optim. 28 (2004), pp. 249–258], we obtain the existence of two intervals of positive real parameters λ for which the above problem admits three weak solutions in , whose norms are uniformly bounded with respect to λ belonging to one of the two open intervals. In particular, we also prove some properties of p(x)-Kirchhoff–Laplace operator.